14 problems

Let $G$ be a finitely generated free-by-cyclic group, meaning a group fitting into an exact sequence … with $F$ a finitely generated free group. A group is (finitely generated free…

A group is locally quasi-convex when every finitely generated subgroup is quasi-convex in the ambient hyperbolic group. A group is virtually a mapping torus of a free group when it…

Let $\mathbb G=\mathbb F\rtimes_\phi\mathbb Z$ and $\mathbb G'=\mathbb F'\rtimes_\psi\mathbb Z$ be free-by-cyclic groups. Let $\mathfrak d(\phi)$ denote the length, or size, of a l…

Let $\mathbb G=\mathbb F\rtimes_\phi\mathbb Z$ and $\mathbb G'=\mathbb F'\rtimes_\psi\mathbb Z$ be free-by-cyclic groups, where an outer automorphism is fully irreducible if it has…

Let $\mathbb G$ and $\mathbb G'$ be quasi-isometric free-by-cyclic groups. A slender splitting is a splitting of a group over a slender subgroup. Slender-splitting conjecture. A sl…

Let $\mathbb G=\mathbb F\rtimes_\phi\mathbb Z$ be a free-by-cyclic group, and suppose that $\phi$ has exponential growth. Let the attracting laminations of $\phi$ be partially orde…

Let $G'$ be a finitely generated free-by-cyclic group, and let $cvarphi\to\Phi$ denote an extension as in the diagram above, where the underlying free groups are finitely generated…

Free-by-cyclic graphical discreteness conjecture. A one-ended, hyperbolic free-by-cyclic group $F_n\rtimes_{\phi}\mathbb{Z}$ with trivial JSJ decomposition is graphically discrete.

Let $\mathbb F$ be a skew-field. The groups and invariants in the paper include the agrarian cohomological dimension $\operatorname{cd}_{\mathbb F}$ and the agrarian Betti numbers…

Let $F_m$ be a finitely generated free group, let $varphi$ be an automorphism, and set … Assume that $varphi$ is polynomially growing of degree $d$. For a Farber sequence…

Chain flare conjecture. The chain flare condition holds whenever the monodromy is exponentially growing.

Quasi-isometric invariance of irreducibility and atoroidality. If $F\rtimes_\phi\mathbb Z$ and $F'\rtimes_\psi\mathbb Z$ are quasi-isometric, then $\phi$ is irreducible and atoroid…

Free-by-cyclic CAT(0) cube complex action conjecture. Every free-by-cyclic group acts freely on a CAT(0) cube complex.

Kapovich's conjecture. Many one-relator groups are finitely generated free-by-cyclic.